Question: Solve for $x$ : $5x^2 + 35x - 150 = 0$
Dividing both sides by $5$ gives: $ x^2 + {7}x {-30} = 0 $ The coefficient on the $x$ term is $7$ and the constant term is $-30$ , so we need to find two numbers that add up to $7$ and multiply to $-30$ The two numbers $10$ and $-3$ satisfy both conditions: $ {10} + {-3} = {7} $ $ {10} \times {-3} = {-30} $ $(x + {10}) (x {-3}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 10) (x -3) = 0$ $x + 10 = 0$ or $x - 3 = 0$ Thus, $x = -10$ and $x = 3$ are the solutions.